How to avoid pinching on concave shapes with the bevel modifier and subsurf?
It's interesting to have a look at why this happens. This is a transition from  2x Simple subdiv to Catmull-Clark subdiv on a corner beveled with one segment.



It's not 'pinching' in the same sense as the pinching you get at say, the poles of a UV Sphere. It's more like 'leapfrogging'. Under the CC algorithm,the edges of small faces that were next to large faces in their own plane move further than small faces that were next to small faces at an angle to them, to the point that they overtake. This effect is compounded with each iteration, and the smaller the bevel by comparison with surrounding faces, the worse it gets.

I've never been able to think of a solution to fully automate away the need for hand-modified holding loops, or using creases to pin vertices and prevent them from being moved by CC.

Personally I tend to think in 3's, (put in a bevel with 2 segments) and not restrict by angle. Then the extra edge-loops an be 'tied off' (reduced from 3 to 1) elsewhere on the model, if needed. But that's still hand work.